Proofgold Proof

Apply unknownprop_50f1b502ede8f73efac5f5638826e50355eb6f972374cae79b4ecf4e1be40675 with ∀ x0 : (ι → ι) → (ι → ι) → (ι → ι) → ι → ι → ο . ∀ x1 : (((ι → ι → ι → ι) → ι → ι) → ((ι → ι → ι) → ι → ι) → ι) → (ι → ι → ι → ι) → ο . ∀ x2 : (((((ι → ι) → ι) → ι) → (ι → ι) → ι) → ι) → ι → ο . ∀ x3 : (((((ι → ι) → ι) → ι) → (ι → ι → ι) → ι) → ι) → ((((ι → ι) → ι) → ι → ι) → ι) → ι → (ι → ι) → ι → ο . ... ⟶ ... ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . In (setsum (Inj1 (Inj0 (x7 (λ x8 : (ι → ι) → ι → ι . 0)))) 0) ... ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . 0) (Inj1 0) ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . x6 (λ x9 x10 . 0) (λ x9 : ι → ι . λ x10 . Inj1 (Inj0 (Inj0 0)))) (Inj1 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . 0) 0 ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . x5) (Inj0 x5)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x3 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι → ι . setsum (Inj0 (setsum (Inj1 0) (setsum 0 0))) (setsum (x7 (λ x9 : (ι → ι) → ι . setsum 0 0)) (setsum 0 0))) (x5 (λ x8 . Inj1 (setsum (Inj0 0) (Inj0 0))) (x7 (λ x8 : (ι → ι) → ι . Inj0 (Inj1 0))) (λ x8 . 0) (Inj0 (Inj0 (Inj0 0)))) (λ x8 . Inj1 x8) (setsum (Inj1 (x5 (λ x8 . x8) (setsum 0 0) (λ x8 . 0) 0)) (Inj1 (Inj1 (x7 (λ x8 : (ι → ι) → ι . 0))))) ⟶ x1 (λ x8 : (ι → ι → ι → ι) → ι → ι . λ x9 : (ι → ι → ι) → ι → ι . 0) (λ x8 x9 x10 . x9)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x7 . x1 (λ x8 : (ι → ι → ι → ι) → ι → ι . λ x9 : (ι → ι → ι) → ι → ι . Inj1 (setsum (setsum 0 0) (Inj0 0))) (λ x8 x9 x10 . setsum x9 (Inj0 (setsum x8 x8))) ⟶ In (setsum (x6 (λ x8 . 0) (λ x8 : ι → ι . λ x9 . Inj0 (setsum 0 0)) x4) (setsum 0 (Inj1 0))) (Inj1 x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 x7 . In (setsum (setsum 0 0) 0) (x5 0 0 (λ x8 . setsum (Inj0 (Inj1 0)) 0)) ⟶ x0 (λ x8 . x6) (λ x8 . 0) (λ x8 . 0) x7 x7 ⟶ x0 (λ x8 . Inj0 0) (λ x8 . Inj1 0) (λ x8 . setsum 0 (x5 0 (setsum (setsum 0 0) (Inj1 0)) (λ x9 . x8))) 0 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . In (setsum (x5 (Inj1 0)) 0) (setsum (Inj0 x7) (Inj1 (setsum x7 (setsum 0 0)))) ⟶ x0 (λ x8 . Inj1 0) (λ x8 . 0) (λ x8 . Inj1 (x5 0)) (x5 (Inj1 0)) 0 ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . setsum 0 (setsum (setsum 0 0) (setsum (Inj0 0) (setsum 0 0)))) (x5 (setsum 0 x4))) ⟶ False.